A resident of the four-plex, located in the 5000 block of Harlow Way, reported the fire at 10:51 a.m., San Jose fire Capt. Mary Gutierrez said.
The two upstairs units sustained substantial fire damage, and the downstairs units had water damage, Gutierrez said.
"It appears (the fire) started in an upstairs unit and it got into the attic space," she said.
The cause of the fire remains under investigation.
Everyone managed to exit the building safely, and no injuries were reported.
Gutierrez said that at the height of the blaze, 42 firefighters were at the scene.